Details

sample108.0ms

Algorithm

intervals

Results

53.0ms	119×	body	1280	valid
26.0ms	29×	body	2560	valid
13.0ms	55×	body	640	valid
3.0ms	18×	body	320	valid
2.0ms	30×	body	80	valid
1.0ms	5×	body	160	valid

simplify5.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	9	4
1	10	4
2	10	4

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 41.0b

localize9.0ms

Local error

Found 2 expressions with local error:

0.7b	(- (sin (+ x eps)) (sin x))
2.9b	(sin (+ x eps))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

4×	`add-sqr-sqrt` `*-un-lft-identity` `add-log-exp`
2×	`pow1` `add-exp-log` `add-cube-cbrt` `sin-sum` `add-cbrt-cube`
1×	`sub-neg` `flip3--` `diff-log` `diff-sin` `associate--l+` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

2 → 24

Calls

2 calls:

20.0ms	(- (sin (+ x eps)) (sin x))
4.0ms	(sin (+ x eps))

series64.0ms

Counts

2 → 6

Calls

2 calls:

45.0ms	(- (sin (+ x eps)) (sin x))
19.0ms	(sin (+ x eps))

simplify140.0ms

Algorithm

egg-herbie

Counts

30 → 30

Iterations

Useful iterations: 2 (10.0ms)

Iter	Nodes	Cost
0	133	175
1	301	166
2	937	164
3	3445	164
4	5001	164

prune87.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 19.2b

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b	(- (* (cos x) (sin eps)) (sin x))
0.1b	(* (cos x) (sin eps))
0.1b	(* (sin x) (cos eps))
2.2b	(+ (* (sin x) (cos eps)) (- (* (cos x) (sin eps)) (sin x)))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt`
11×	`add-log-exp`
8×	`pow1` `add-exp-log` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube`
6×	`associate-r` `associate-l`
3×	`sin-cos-mult`
2×	`sub-neg` `associate-+r+` `flip3--` `diff-log` `pow-prod-down` `frac-add` `prod-exp` `sum-log` `*-commutative` `flip--` `cbrt-unprod` `unswap-sqr`
1×	`+-commutative` `associate-+r-` `flip3-+` `flip-+`

Counts

4 → 66

Calls

4 calls:

4.0ms	(- (* (cos x) (sin eps)) (sin x))
4.0ms	(* (cos x) (sin eps))
4.0ms	(* (sin x) (cos eps))
14.0ms	(+ (* (sin x) (cos eps)) (- (* (cos x) (sin eps)) (sin x)))

series264.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(- (* (cos x) (sin eps)) (sin x))
48.0ms	(* (cos x) (sin eps))
42.0ms	(* (sin x) (cos eps))
110.0ms	(+ (* (sin x) (cos eps)) (- (* (cos x) (sin eps)) (sin x)))

simplify43.0ms

Algorithm

egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	348	614
1	1352	581
2	5002	565

prune252.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.5b

localize20.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (sin x) (- (cos eps) 1))
0.1b	(* (cos x) (sin eps))
0.2b	(+ (* (sin x) (- (cos eps) 1)) (* (cos x) (sin eps)))
2.9b	(- (cos eps) 1)

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
14×	`*-un-lft-identity`
10×	`associate-r`
8×	`pow1` `add-exp-log` `add-cube-cbrt` `add-cbrt-cube` `add-log-exp`
6×	`associate-l`
5×	`sub-neg`
4×	`distribute-rgt-in` `associate-+l+` `distribute-lft-in` `difference-of-squares`
2×	`flip3--` `difference-of-sqr-1` `associate-r/` `pow-prod-down` `prod-exp` `-commutative` `flip--` `cbrt-unprod` `distribute-lft-out--` `unswap-sqr`
1×	`+-commutative` `flip3-+` `diff-log` `sum-log` `flip-+`

Counts

4 → 77

Calls

4 calls:

11.0ms	(* (sin x) (- (cos eps) 1))
4.0ms	(* (cos x) (sin eps))
7.0ms	(+ (* (sin x) (- (cos eps) 1)) (* (cos x) (sin eps)))
3.0ms	(- (cos eps) 1)

series224.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(* (sin x) (- (cos eps) 1))
49.0ms	(* (cos x) (sin eps))
112.0ms	(+ (* (sin x) (- (cos eps) 1)) (* (cos x) (sin eps)))
18.0ms	(- (cos eps) 1)

simplify44.0ms

Algorithm

egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	337	548
1	1280	501
2	5002	499

prune471.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.1b

localize19.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cos x) (sin eps))
0.2b	(+ (* (sin x) (log (exp (- (cos eps) 1)))) (* (cos x) (sin eps)))
2.8b	(log (exp (- (cos eps) 1)))
2.9b	(- (cos eps) 1)

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
16×	`*-un-lft-identity`
15×	`log-prod`
10×	`add-cube-cbrt` `associate-+l+`
8×	`log-pow` `add-log-exp`
7×	`pow1` `exp-prod`
6×	`add-exp-log` `exp-sum` `add-cbrt-cube`
5×	`distribute-rgt-in` `distribute-lft-in`
4×	`sub-neg` `difference-of-squares`
3×	`associate-r` `associate-l`
2×	`difference-of-sqr-1` `distribute-lft-out--`
1×	`+-commutative` `log-div` `flip3--` `flip3-+` `exp-diff` `diff-log` `rem-log-exp` `pow-prod-down` `prod-exp` `sum-log` `*-commutative` `flip--` `cbrt-unprod` `flip-+` `unswap-sqr`

Counts

4 → 77

Calls

4 calls:

4.0ms	(* (cos x) (sin eps))
14.0ms	(+ (* (sin x) (log (exp (- (cos eps) 1)))) (* (cos x) (sin eps)))
8.0ms	(log (exp (- (cos eps) 1)))
3.0ms	(- (cos eps) 1)

series201.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(* (cos x) (sin eps))
119.0ms	(+ (* (sin x) (log (exp (- (cos eps) 1)))) (* (cos x) (sin eps)))
21.0ms	(log (exp (- (cos eps) 1)))
19.0ms	(- (cos eps) 1)

simplify154.0ms

Algorithm

egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 3 (144.0ms)

Iter	Nodes	Cost
0	332	594
1	1101	541
2	4598	519
3	5001	517

prune279.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.1b

regimes125.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	10
1	15	10

end0.0ms

sample2.9s

Algorithm

intervals

Results

1.4s	3317×	body	1280	valid
613.0ms	663×	body	2560	valid
444.0ms	1852×	body	640	valid
125.0ms	746×	body	320	valid
63.0ms	1076×	body	80	valid
36.0ms	346×	body	160	valid